Results 51 to 60 of about 740 (152)
A generalised Nehari manifold method for a class of non linear Schrodinger systems in R3
, 2021 The aim of this thesis is to study a generalisation of the Nehari manifold method applied to a class of non linear Schrodinger systems. In particular, we consider stationary solutions so that the problem becomes elliptic.
CORTOPASSI, TOMMASO
core
Ground states of a non‐local variational problem and Thomas–Fermi limit for the Choquard equation
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract We study non‐negative optimisers of a Gagliardo–Nirenberg‐type inequality ∫∫RN×RN|u(x)|p|u(y)|p|x−y|N−αdxdy⩽C∫RN|u|2dxpθ∫RN|u|qdx2p(1−θ)/q,$$\begin{align*} & \iint\nolimits _{\mathbb {R}^N \times \mathbb {R}^N} \frac{|u(x)|^p\,|u(y)|^p}{|x - y|^{N-\alpha }} dx\, dy\\ &\quad \leqslant C{\left(\int _{{\mathbb {R}}^N}|u|^2 dx\right)}^{p\theta } {\
Damiano Greco +3 more
wiley +1 more source
Planar Choquard equations with critical exponential reaction and Neumann boundary condition
Mathematische Nachrichten, Volume 297, Issue 10, Page 3847-3869, October 2024.Abstract We study the existence of positive weak solutions for the following problem: −Δu+α(x)u=∫ΩF(y,u)|x−y|μ1dyf(x,u)inΩ,∂u∂η+βu=∫∂ΩG(y,u)|x−y|μ2dνg(x,u)on∂Ω,$$\begin{equation*} \begin{aligned} \hspace*{65pt}-\Delta u + \alpha (x) u &= {\left(\int \limits _{\Omega }\frac{F(y,u)}{|x-y|^{{\mu _1}}}\;dy\right)}f(x,u) \;\;\text{in} \; \Omega,\\ \hspace ...
Sushmita Rawat +2 more
wiley +1 more source
Non‐autonomous double phase eigenvalue problems with indefinite weight and lack of compactness
Bulletin of the London Mathematical Society, Volume 56, Issue 2, Page 734-755, February 2024.Abstract In this paper, we consider eigenvalues to the following double phase problem with unbalanced growth and indefinite weight, −Δpau−Δqu=λm(x)|u|q−2uinRN,$$\begin{equation*} \hspace*{3pc}-\Delta _p^a u-\Delta _q u =\lambda m(x)|u|^{q-2}u \quad \mbox{in} \,\, \mathbb {R}^N, \end{equation*}$$where N⩾2$N \geqslant 2$, 1
Tianxiang Gou, Vicenţiu D. Rădulescu
wiley +1 more source
Ground states for Schrodinger-Poisson systems with three growth terms
Electronic Journal of Differential Equations, 2014 In this article we study the existence and nonexistence of ground states of the Schrodinger-Poisson system $$\displaylines{ -\Delta u+V(x)u+K(x)\phi u=Q(x)u^3,\quad x\in \mathbb{R}^3,\cr -\Delta\phi=K(x)u^2, \quad x\in \mathbb{R}^3, }$$ where V ...
Hui Zhang, Fubao Zhang, Junxiang Xu
doaj
Second-order derivative of domain-dependent functionals along Nehari manifold trajectories
, 2020 Assume that a family of domain-dependent functionals EΩt EΩt possesses a corresponding family of least energy critical points ut which can be found as (possibly nonunique) minimizers of EΩt EΩt over the associated Nehari manifold N(Ωt) N ...
Kolonitskii, Sergey +3 more
core +1 more source
Journal of Function Spaces, Volume 2024, Issue 1, 2024.In this paper, we consider the weighted m‐biharmonic equation with nonlinear damping and source terms. We proved the global existence of solutions. Later, the decay of the energy is established by using Nakao’s inequality. Finally, we proved the blow‐up of solutions in finite time.
Ayşe Fidan +3 more
wiley +1 more source
, 2018 This paper is concerned with variational continuation of branches of solutions for nonlinear boundary value problems, which involve the p p -Laplacian, an indefinite nonlinearity, and depend on a real parameter λ \lambda
Kaye Silva, Yavdat Ilyasov
core +1 more source
Ground state solution of a nonlocal boundary-value problem
Electronic Journal of Differential Equations, 2013 In this article, we apply the Nehari manifold method to study the Kirchhoff type equation $$ -\Big(a+b\int_\Omega|\nabla u|^2dx\Big)\Delta u=f(x,u) $$ subject to Dirichlet boundary conditions.
Cyril Joel Batkam
doaj
Multiplicity of Solutions for a Class of Kirchhoff–Poisson Type Problem
Abstract and Applied Analysis, Volume 2024, Issue 1, 2024.In this paper, we use the fountain theorems to investigate a class of nonlinear Kirchhoff–Poisson type problem. When the nonlinearity f satisfies the Ambrosetti–Rabinowitz’s 4‐superlinearity condition, or under some weaker superlinearity condition, we establish two theorems concerning with the existence of infinitely many solutions.
Ziqi Deng +2 more
wiley +1 more source